Non-fragile attitude control method for morphing aircraft based on quantized switching mechanism

Abstract

The application provides a metamorphic aircraft non-friable attitude control method based on a quantization switching mechanism, relates to the field of aircraft control technology, and comprises the following steps: acquiring a deformation amount of a metamorphic aircraft, quantizing and discretizing the deformation amount through a quantization switching mechanism to obtain different quantization modes; acquiring outer loop state variables of the aircraft corresponding to the quantization modes, and calculating a virtual control law according to the outer loop state variables; wherein the outer loop state variables include an attack angle, a roll angle, a pitch angle and a deformation rate, and the virtual control law is designed according to a barrier Lyapunov function for avoiding friability; acquiring inner loop state variables of the aircraft corresponding to the quantization modes, and calculating control variables according to the inner loop state variables; wherein the inner loop state variables include a roll angular velocity, a yaw angular velocity, a pitch angular velocity and a deformation rate change rate; and performing attitude control on the metamorphic aircraft through the control variables, so that the application can improve the control stability and safety of HMVs under complex flight conditions.

Description

Technical Field

[0001] This invention relates to the field of aircraft control technology, and more specifically, to a non-fragile attitude control method for variable-structure aircraft based on a quantization switching mechanism. Background Technology

[0002] Depending on the flight mission and environment, hypersonic morphing vehicles (HMVs) can maintain good aerodynamic performance by changing their configuration. While this change brings good aerodynamic performance, it also significantly alters the aerodynamic parameters in the model, increasing model uncertainty. Similarly, during large envelope flight, changes in the environment (such as wind disturbance and atmospheric density) also increase model uncertainty. These uncertainties pose challenges to HMV modeling and controller design.

[0003] To alleviate the aforementioned modeling difficulties at the configuration design level, current HMVs mainly employ deformation methods such as variable sweep, extended length, and variable camber, with variable sweep wings being a typical example due to their aerodynamic adaptability across a wide speed range. However, traditional switching mechanisms lack a clear quantitative description of the modal transition process, and their instantaneous switching behavior can easily excite unmodeled high-frequency dynamics and jeopardize system stability. Therefore, how to introduce an effective quantification mechanism during the switching process to achieve a description of modal transitions is a key problem that urgently needs to be solved in current modeling research.

[0004] In summary, while HMVs can proactively modify their aerodynamic shape to optimize full-profile performance based on flight missions and environments, this deformation process leads to significant changes in aerodynamic parameters and introduces additional forces and moments, greatly increasing the uncertainty and modeling difficulty of the system model. Furthermore, typical deformation methods such as variable sweep angles cause continuous transitions between different configurations, exhibiting strong nonlinearity and multimodal characteristics, making traditional single-model-based control methods difficult to apply. In addition, the aircraft is subject to strict state constraints such as angle of attack and overload during flight. Existing methods are prone to drastic increases in control output or even controller singularities when tracking errors approach constraint boundaries. Existing disturbance observer methods typically use fixed conservative upper bounds to suppress lumped disturbances, and the constraint envelope cannot adaptively adjust according to error changes, resulting in insufficient robustness and dynamic constraint satisfaction of the control system. Therefore, there is an urgent need for a control method that can simultaneously address multimodal switching, state constraint satisfaction, and unknown disturbance suppression during deformation to improve the control stability and safety of HMVs under complex flight conditions. Summary of the Invention

[0005] In view of this, the present invention proposes a non-fragile attitude control method for variable-structure aircraft based on a quantization switching mechanism to solve the problems existing in the prior art.

[0006] To achieve the above objectives, this invention proposes a non-fragile attitude control method for variable-structure aircraft based on a quantization switching mechanism, comprising: The deformation amount of the variable-structure aircraft is obtained, and the deformation amount is quantized and discretized through a quantization switching mechanism to obtain different quantization modes; The outer loop state variables of the aircraft corresponding to the quantized modes are obtained, and the virtual control law is calculated based on the outer loop state variables. The outer loop state variables include angle of attack, roll angle, pitch angle and deformation rate. The virtual control law is designed based on the obstacle Lyapunov function for vulnerability avoidance. The inner loop state variables of the aircraft corresponding to the quantized modes are obtained, and the control variables are calculated based on the inner loop state variables; wherein the inner loop state variables include roll rate, yaw rate, pitch rate and deformation rate of change. The attitude of the modified aircraft is controlled by controlling variables.

[0007] Optionally, the quantization switching mechanism is as follows: ,in, This represents the quantization mode corresponding to time step t. Indicates the partitioning variable, This represents the deformation rate.

[0008] Optionally, the calculation process of the virtual control rate includes:

[0009] in, This indicates the desired angular rate command output by the outer loop. For the first Tracking error of the outer loop state quantity of each channel For feedback gain, Nonlinear functions of the outer loop state variables For the online estimate of uncertainty, where The outer ring weight parameter is adjustable. For the basis function vector, For the upper bound of the composite polynomial, For the safety repulsion coefficient, This is the error amplification factor. This is the control gain matrix.

[0010] Optionally, the calculation of the virtual control law also includes the calculation of the adaptive law and the upper bound estimate; The adaptive law is as follows:

[0011] The upper bound is estimated as follows:

[0012] in, It is the estimated value of the fuzzy weight of the j-th channel. The rate of change, For adaptive learning rate, This is the error amplification factor. For fuzzy basis function vectors; It is the first Channel composite polynomial upper bound estimate The rate of change, Estimate the learning rate for the upper bound. and For the same error amplification factor, These are the adjustment parameters for the hyperbolic tangent function; subscripts j=1,2,3,4 correspond to the four channels: angle of attack, sideslip angle, roll angle, and deformation rate, respectively. Indicates the current quantization mode, through Adjustment ,pass Adjustment , will the and Calculate the corresponding virtual control law.

[0013] Optionally, the calculation process of the control quantity includes:

[0014] in, To control the quantity, For the first The tracking error of the inner loop state variables of each channel. For feedback gain, Nonlinear functions of inner loop state variables For the online estimate of uncertainty, where The inner loop weighting parameter is adjustable. For the basis function vector, For the upper bound of the composite polynomial, This is the control gain matrix.

[0015] Optionally, the calculation of the control variable may also include the calculation of the corresponding adaptive law and upper bound estimate: The adaptive law is:

[0016] The upper bound is estimated as follows:

[0017] in, It is the estimated value of the fuzzy weight of the j-th channel. The rate of change, For adaptive learning rate, For the first The tracking error of the inner loop state variables of each channel. For fuzzy basis function vectors; It is the first Channel composite polynomial upper bound estimate The rate of change, Estimate the learning rate for the upper bound. These are the adjustment parameters for the hyperbolic tangent function; the subscripts j=1,2,3,4 correspond to the four channels of roll rate, yaw rate, pitch rate, and rate of change of deformation, respectively. Indicates the current quantization mode, through Adjustment ,pass Adjustment , will the and Calculate the corresponding virtual control law.

[0018] Optionally, the barrier Lyapunov function for vulnerability avoidance is:

[0019] in, The barrier function for four state channels, real-time safety boundary. , Let be the constraint boundary function, where the constraint boundary exponential convergence rate is . The initial constraint boundary magnitude and the steady-state constraint boundary magnitude are respectively , This is an adjustment function with a correction term.

[0020] Optional, adjustment function for:

[0021] Among them, boundary adjustment gain Adjustment term decay rate Boundary trigger threshold coefficient These are design parameters.

[0022] On the other hand, the present invention provides a non-fragile attitude control system for a variable-structure aircraft based on a quantization switching mechanism for performing the above-described method.

[0023] Compared with the prior art, the beneficial effects of the present invention are as follows: Compared with the prior art, the present invention has achieved the following beneficial technical effects in many aspects: This invention introduces modal partitioning variables and combines them with a deformation rate design quantization switching mechanism to quantize the continuous deformation process of a hypersonic morphing vehicle into a finite number of discrete modes. The vehicle maintains modal constancy while the deformation rate continuously changes, and mode switching only occurs when the deformation rate reaches a specific threshold. This effectively avoids control surface jitter and flight attitude oscillations caused by frequent switching, ensuring a smooth transition of flight quality during deformation and significantly improving the stability of the flight control system.

[0024] The vulnerability avoidance obstacle Lyapunov function (FABLFs) method constructed in this invention can adaptively adjust the constraint envelope in real time based on the magnitude of the tracking error. When the aircraft's attitude error approaches the safety boundary due to large maneuvers or sudden disturbances, FABLFs adjusts the constraint envelope in a timely manner, avoiding the risk of control surface saturation or even controller failure caused by the fixed envelope in traditional BLFs methods. It provides a higher safety margin for the aircraft while ensuring that state constraints such as angle of attack and sideslip angle are never violated. Comparative simulations with traditional BLFs methods show that traditional methods cause significant fluctuations in attitude error and singular controller outputs during command jumps due to the fixed constraint envelope, while the method of this invention can handle these situations smoothly, resulting in smooth convergence of the flight attitude.

[0025] This invention treats various uncertainties encountered by an aircraft during deformation, such as external wind disturbances, changes in atmospheric density, and aerodynamic parameter perturbations, into a single composite polynomial. An online estimation and real-time compensation are then performed using a perturbation upper bound estimator. Simulation results show that even under severe conditions of aerodynamic parameter bias (30% atmospheric density bias and 15% moment of inertia bias) and at the instant of a step change in command, the perturbation upper bound estimate responds quickly, ensuring that the aircraft's attitude does not exhibit severe chattering, control surface deflection is smooth, and tracking accuracy meets engineering requirements. This significantly enhances the aircraft's survivability and mission completion capabilities in complex environments.

[0026] This invention rigorously guarantees the stability of the closed-loop system using Lyapunov stability theory, ensuring that the attitude angle tracking error converges exponentially to a small neighborhood near the origin throughout the entire deformation process (the deformation mechanism operates at full speed), and that the angular rate accurately tracks the virtual control law. Simulations verify the comprehensive performance of the proposed control strategy in terms of mode switching, state constraint satisfaction, and anti-interference capability, demonstrating promising prospects for engineering applications. Attached Figure Description

[0027] Various other advantages and benefits will become apparent to those skilled in the art upon reading the following detailed description of preferred embodiments. The accompanying drawings are for illustrative purposes only and are not intended to limit the invention. In the drawings: Figure 1This is a schematic diagram of variable sweep wing HMVs in an embodiment of the present invention; Figure 2 This is a flowchart of the non-fragile fuzzy control based on the quantization switching mechanism in an embodiment of the present invention; Figure 3 This is the attitude angle and deformation rate tracking curve in an embodiment of the present invention; Figure 4 This is the angular rate tracking curve in an embodiment of the present invention; Figure 5 This is a comparison curve of envelope constraints in an embodiment of the present invention; Figure 6 This is a schematic diagram of the interference upper bound estimator in an embodiment of the present invention; Figure 7 This is a graph showing the controller output curve in an embodiment of the present invention. Detailed Implementation

[0028] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided to enable a more thorough understanding of the present disclosure and to fully convey the scope of the disclosure to those skilled in the art. It should be noted that, unless otherwise specified, the embodiments and features described herein can be combined with each other. The present invention will now be described in detail with reference to the accompanying drawings and embodiments.

[0029] To address the uncertainties caused by deformation in hypersonic morphing vehicles (HMVs) under state constraints, a non-fragile control strategy based on a quantization switching mechanism is proposed. First, to describe the deformation characteristics, a quantization switching mechanism is designed in conjunction with modal partitioning variables, quantizing the deformation process into a finite number of discrete modes, thereby establishing an HMV model based on the quantization switching mechanism. Second, a vulnerability-avoidance barrier Lyapunov function is constructed to prevent the "fragility" problem of a sharp increase in control output when the tracking error approaches the constraint envelope, ensuring that the controller does not exhibit singular phenomena. Building upon this, to address model uncertainties and external disturbances caused by configuration changes, a fuzzy logic system is used to approximate the unknown nonlinear terms, coupling the approximation error, external disturbances, and the differential of the virtual controller into a composite polynomial, which is compensated for by designing a disturbance upper bound estimator. Finally, based on Lyapunov stability theory, it is proven that all signals in the closed-loop system are bounded, the tracking error converges to a small neighborhood near the origin, and the state constraints are not violated. Simulation results verify the effectiveness of the proposed control strategy.

[0030] This invention constructs a non-fragile fuzzy control method based on a quantization switching mechanism, and its main contributions can be summarized in the following three aspects: 1) Unlike the LPV method, this method introduces modal partitioning variables to characterize the deformation feature. Based on the modal partitioning fineness, combined with the deformation rate, a modeling method based on quantization switching mechanism is proposed. This method realizes the quantitative description of the modal transition process and provides a model basis for the controller design of morphing aircraft.

[0031] 2) To avoid controller singularity caused by the BLFs method when the tracking error approaches the constraint envelope, the FABLFs method was constructed. This method combines the magnitude of the tracking error with envelope sensing and adjustment technology, which solves the controller singularity problem caused by BLFs and improves the stability of the control system while ensuring that the state constraints are satisfied.

[0032] 3) The difference from existing disturbance observer control methods lies in the way uncertainties are handled. Existing methods typically employ a scaling approach, using a fixed, conservative upper bound to suppress lumped disturbances. This paper, however, designs a compensation strategy based on upper bound estimation. This strategy couples external disturbances, approximation errors, and virtual control differentials into a composite polynomial, and then obtains its boundary information by constructing a disturbance upper bound estimator.

[0033] 1. HMVs related models and switching mechanisms 1.1. HMVs Model This invention focuses on variable-sweep wing hypersonic morphing vehicles (HMVs), such as... Figure 1 As shown. To design an attitude controller for HMVs, a deformation rate is introduced. Characterizing the dynamic evolution of an aircraft configuration, its definition is as follows: , (1) In the formula: For the sweep angle, where and These correspond to the minimum sweep angle and the maximum sweep angle, respectively. The moment of inertia of the actuator. The equivalent viscous damping coefficient of the actuator. This is the equivalent control input for the actuator. This represents the unmodeled dynamics of the actuator and external disturbances. Based on the aforementioned deformation rates, an HMVs model is established as follows:

[0034]

[0035] In the formula: For the angle of attack, Sideslip angle, The tilt angle, The pitch angle, For the roll angular velocity, Yaw angular velocity, Let be the pitch angular velocity, where the superscript · indicates the corresponding derivative and the corresponding rate of change. These are flight speed, aircraft mass, and gravitational acceleration, respectively, with moment of inertia being... ,in Represented by the xyz directions, the dynamic pressure is... , Atmospheric density, This is the reference area before deformation. This is the lateral reference length of the wing. This is the longitudinal reference length of the wing. These are the additional forces and moments in the x, y, and z directions caused by deformation; these model uncertainties will be approximated later using FLSs. Furthermore, For lift, It is a lateral force. For rolling torque, For yaw moment, Let be the pitching moment, where the aerodynamic coefficient is expressed as follows:

[0036]

[0037] (4)

[0038]

[0039] In the formula: The deflection angle of the aerodynamic control surface. Here are the aerodynamic coefficients related to Mach number Ma and angle of attack α, with subscripts L and N representing the corresponding lift and lateral forces, x, y, and z representing the corresponding directions, and superscript parameters indicating the parameters they correspond to. C represents the aerodynamic coefficient related to Mach number, and m represents the aerodynamic coefficient related to angle of attack. Next, the state vector is defined. The HMVs model in equations (2)-(3) is transformed into the following state-space equations: (5) In the formula, , , and It is a nonlinear function. and For uncertain terms, and The interference term is expressed as follows: (6) (7) (8) (9) (10) (11) 1.2 Fuzzy Model Based on Quantization Switching Mechanism To characterize this deformation property, modal partitioning variables are introduced. Combined with deformation rate The following quantization switching mechanism is obtained: (12) Simultaneously, FLSs are introduced to approximate the unknown nonlinear dynamics and unmodeled dynamics caused by deformation in the system online. Considering the characteristics of attitude control for variable-structure aircraft, an IF-THEN fuzzy rule base of the following form is established:

[0040] (13) in, As input variables for FLSs, they can represent angle of attack, sideslip angle, pitch angle, and deformation state; fuzzy sets Linguistic variables defined on the error domain of each state, such as "negative large (NB)", "zero (ZO)", "positive large (PB)", etc., are used to describe the magnitude level of each state error; fuzzy sets For output variables The language level corresponds to the compensation value of the virtual control variable. The format is: (14) in, It represents the degree to which an input vector belongs to the corresponding fuzzy set (membership degree). For the first The online estimate of the compensation amount of the uncertainty term corresponding to the fuzzy rule is the predicted amplitude of the unmodeled dynamic under the working condition covered by the rule.

[0041] Furthermore, the fuzzy basis function is defined as follows: (15) in, This indicates the activation strength of the current state belonging to the q-th fuzzy rule, and its physical meaning is the degree of matching of the current flight state with the q-th typical uncertain working condition.

[0042] In the formula, let the parameter vector fuzzy basis function vector Based on the above definition, FLSs can be written as: .

[0043] Lemma 1: Suppose a continuous mapping Defined in compact set Above, for any constant There exists a corresponding FLSs such that:

[0044] According to Lemma 1, for compact sets any continuous function on and given constants There exists an optimal parameter vector. ,satisfy:

[0045] In the formula, To approximate the error, and satisfy... Based on the above analysis, for There are always unknown normal numbers. This makes the approximation error ,satisfy .

[0046] Based on this, the uncertainties and They can be represented as:

[0047] (18) Adaptive weight parameters

[0048] Basis function vectors of fuzzy functions

[0049] constant , Similarly.

[0050] The four components correspond to the additional forces / torques on the pitch, yaw, roll and deformation channels of HMVs, respectively, which are caused by the reduction of control surface efficiency due to aerodynamic heat under high-speed flight, the shift of pressure center caused by shock wave position shift, and the aerodynamic shape change caused by the extension and contraction of deformation mechanism. This represents the real-time perturbation of the inertial and Coriolis matrices caused by changes in wing sweep angle or span, a dynamic that changes drastically with changes in the deformed configuration. This invention is based on a fuzzy logic system and updates the fuzzy rule basis parameters online. , The above nonlinear disturbances are dynamically fitted, and the fitting results are superimposed on the control commands of the control surfaces and deformation mechanism actuators as feedforward compensation. This directly adjusts the output of each channel actuator, physically offsetting the negative impact of aerodynamic and thermal effects and configuration changes on flight stability in each control cycle, ensuring that the aircraft maintains controllable attitude during large-scale deformation maneuvers across the speed range.

[0051] Among the above parameters In this context, 1 represents x1, 2 represents the second channel in the state vector, and so on. Therefore, equation (5) can be rewritten as:

[0052] (19) Among them, in the outer ring equation, It is the rate of change of attitude angles (angle of attack / slip angle / roll angle / deformation rate), the first term on the right. It is a known nonlinear function that can be precisely calculated, such as gravity or aerodynamic force; the second term... It is the additional force and unknown aerodynamic changes brought about by the deformation of the fuzzy logic system. Online estimates (of which) It is the conclusion weight vector of the fuzzy rule. The third term is a guessed value obtained by multiplying the basis function vectors calculated from the current state (the dot product of the two is used to obtain the guessed value). It is the residual error that the fuzzy system did not guess correctly (assuming it is bounded but the specifics are unknown), the fourth term. Indicates the inner loop angular rate Through coupling matrix Drive the outer ring angle to change, finally These are external disturbances such as wind disturbance; in the inner loop equations, It is the rate of change of angular velocity. These are known terms such as moment of inertia. It is an online estimation of inertial uncertainty by inner-loop FLSs. It is the residual error of the inner loop fuzzy approximation. Indicates the control surface deflection angle command Through the gain matrix The torque is generated, which changes the angular rate. It refers to the disturbance outside the inner ring; all with subscripts The quantities all represent the corresponding values ​​under the discrete quantization mode determined by the quantization switching mechanism based on the deformation rate. The entire model is essentially the sum of "the known part that can be accurately calculated + the unknown part that the fuzzy system guesses online + residual error + interlayer coupling / control input + external disturbance". This model is the common basis for controller design (Section 2.2) and stability proof (Section 3).

[0053] Combining equation (19), the tracking error is defined. and for: (20) in, To track the desired trajectory, This is a virtual control law.

[0054] Assumption 1: Desired tracking trajectory If a function is bounded, then all its derivatives are bounded; that is, there exist positive constants. This makes it possible for the The set consisting of its first and second derivatives satisfy:

[0055] Assumption 2: Control gain matrix Unknown, there exists an unknown positive constant. ,satisfy:

[0056] Lemma 2: For any and any positive constant There exists a constant ,make Established.

[0057] Lemma 3: For BLFs, for any satisfying The variables are subject to the following inequality constraints: .

[0058] Note 1: If the deformation rate is constant, it indicates no configuration change during flight; otherwise, the value of k determines the fineness of the mode division for the variable-sweep wing aircraft. A larger k results in a finer division, and vice versa. Assumption 1 is a conventional assumption for backstepping design. Assumption 2 utilizes the lower bound of eigenvalues ​​to ensure the negative definiteness of the derivative of the Lyapunov function, thereby ensuring system stability; simultaneously, it uses the upper bound of the norm to scale the coupling terms, providing a basis for adaptive law design.

[0059] 2. Controller Design This section describes the design process of the proposed controller. To address the system state constraint problem, Section 2.1 introduces a FABLFs method. By embedding an adaptive adjustment mechanism into BLFs, it effectively avoids control singularities caused by improper selection of fixed boundary parameters. Building upon this, and combining FLSs to approximate unknown nonlinear dynamics, Section 2.2 designs a nonfragile fuzzy controller based on a quantization switching mechanism. The two design parts are interconnected: the former provides a safety guarantee for the system to satisfy state constraints, while the latter, based on this, achieves nonfragile robust control, together forming a complete nonfragile control framework.

[0060] 2.1. Barriers to Vulnerability Avoidance: Lyapunov Function To address the nonfragile attitude control problem, FABLFs are proposed, in the form of: (twenty one) In the formula, The barrier function for four state channels, real-time safety boundary. , Let be the constraint boundary function, where the constraint boundary exponential convergence rate is . The initial constraint boundary magnitude and the steady-state constraint boundary magnitude are respectively These are all design parameters. The adjustment function with a correction term has the following specific form: (twenty two) In the formula, the boundary adjustment gain Adjustment term decay rate Boundary trigger threshold coefficient These are design parameters.

[0061] 2.2. Design of a Non-Fragile Fuzzy Controller Based on Quantization Switching Mechanism This paper proposes a structure for a nonfragile fuzzy controller based on a quantization switching mechanism, as follows: Figure 2 As shown. The detailed design process is as follows: Step 1: Combining equations (19) and (21), we can obtain and The derivative is: (twenty three) (twenty four)

[0062] in, for The row vector,

[0063] make ,like ,but Conversely, if ,Depend on and It can be deduced , Representing a polynomial The upper bound of the bound, the estimated value of which is And satisfy Therefore, the candidate Lyapunov function is: (25) In the formula, and All are design parameters. Combine equation (24) and substitute... ,right Differentiation yields:

[0064] (26) Design virtual control laws using equation (26) , and The upper bound estimates for the adaptive law and the composite polynomial are as follows: (27) (28) (29) In the formula, For the design parameters, in formula (27), This indicates the desired angular rate command output by the outer loop. For the first Outer loop tracking error of each channel For feedback gain, Given a nonlinear function For the online estimate of the model uncertainty of the fuzzy system (where For adaptive weights, (the basis functions of the fuzzy function). This is an estimate of the upper bound of the composite polynomial. The safety repulsion coefficient generated by FABLFs, (Right now () represents the error amplification factor. , The inverse of the control gain matrix; in formula (28), The rate of change of the fuzzy weight estimate. For adaptive learning rate, This is the error amplification factor. For the fuzzy basis function vector; in formula (29), To prevent interference with the rate of change of the upper bound estimate, For learning rate, It is the hyperbolic tangent function. The adjustment parameter for the hyperbolic tangent function; subscript These correspond to the four channels: angle of attack, sideslip angle, tilt angle, and deformation rate, respectively. (Subscripts are also provided.) This indicates the current quantization mode, the superscript ^ indicates the online estimate, and the superscript · indicates the derivative with respect to time.

[0065] Using Young's inequality and Assumption 1, we can deduce that The relation is: (30) Substituting equations (27)-(30) into equation (26) and simplifying, we get: (31) By Lemma 2, Then the simplified form of equation (31) is: (32) Step 2: Combining equation (19), we can obtain The derivative is:

[0066] (33) In the formula, ,in, For polynomials The upper bound of the bound, the estimated value of which is And satisfy Therefore, the candidate Lyapunov function is: (34) In the formula, and These are design parameters.

[0067] Equation (33) and Substitute into equation (34) and... Differentiation yields:

[0068] Then, a nonfragile fuzzy controller based on a quantization switching mechanism. , and The upper bound estimates for the adaptive law and the composite polynomial are as follows: (36) (37) (38) In the formula, For the design parameters. Substituting equations (36)-(38) into (35), and combining with Lemma 2, we can simplify to obtain for: (39) 3. Stability Analysis This section further analyzes the stability of the closed-loop system. Based on the sufficiency conditions given in Theorem 1, and considering factors such as quantization error, switching signals, and controller parameter perturbations, it is demonstrated that the closed-loop system can meet the given stability requirements under the action of the designed non-fragile fuzzy controller based on the quantization switching mechanism.

[0069] Theorem 1: Under the condition that Assumptions 1-2 are satisfied, for the HMVs model, a virtual control law (27), a non-fragile fuzzy controller based on a quantization switching mechanism (36), upper bound estimates of composite polynomials (29), (38), and adaptive laws (28), (37) are adopted. Positive controller design parameters are selected. Make And for any If the initial conditions are satisfied ,but: (i) All signals in the closed-loop system satisfy the semi-globally consistent eventually bounded condition; (ii) The state constraints are not violated.

[0070] Proof: Construct candidate Lyapunov functions for the closed-loop system: (40) Substitute equations (32) and (39) into equation (40), and then... The derivative can be simplified to: (41) make Let be a positive parameter. Equation (41) can be transformed into the following form: (42) Multiply both sides of equation (42) by and in the interval Integrating, we get: (43) Based on the above equation, the stability of the closed-loop system can be proven. Specifically, for any bounded initial conditions... From equation (43), it can be seen that when At that time, the exponent term , The exponential convergence to the bounded set ;right , This means that the closed-loop system is stable.

[0071] because It includes the barrier Lyapunov function term and the parameter estimation error term. Therefore, all signals of the closed-loop system... It satisfies semi-global consistency and eventual boundedness.

[0072] Tracking error Converging the exponent into a bounded compact set satisfies the condition that... Combining the relationship between state variables and tracking error And the expected tracking trajectory in Hypothesis 1 . We can obtain This can further prove that the state constraints are not violated.

[0073] Note 2: The selection of parameters has a significant impact on system performance; therefore, the following analysis is performed. Increase... It can accelerate the convergence of the boundary from the initial amplitude to the steady-state amplitude, and increase... It can enhance the response speed of the constraint boundary to tracking error fluctuations, but larger parameters can lead to excessive boundary expansion and reduce control performance. Determine when to trigger constraint boundary adjustments. The smaller the value, the faster the constraint boundary adjusts, the lower the sensitivity of the constraint boundary to tracking error fluctuations, and the stricter the triggering conditions for boundary adjustment, thereby reducing unnecessary boundary fluctuations; conversely, as the value increases... Increasing the value of the boundary adjustment will increase the number of adjustments, making the constraint more adaptable, but it may also trigger boundary oscillations. It can accelerate the convergence of fuzzy parameters, but if it is too large, it can easily cause oscillations in parameter estimation. and Together they affect the disturbance compensation performance and increase This allows the estimated upper bound of the disturbance to quickly approach the true value.

[0074] 4. Simulation Verification This section describes the simulation conducted in the MATLAB / Simulink environment on a computer equipped with an Intel Core i9-14900HX processor, with a sampling interval of 0.001s. The parameters of the HMVs model can be set based on existing experiments and literature. The total mass of the aircraft is [not specified in the original text]. wing mass gravitational acceleration Reference area The lateral reference length of the wing is The longitudinal reference length of the wing is Moment of inertia , , Moment of inertia of deformation mechanism Simulation conditions: Initial flight altitude set. Initial flight speed .

[0075] The initial value is set as: angle of attack Sideslip angle Tilt angle Deformation rate The initial values ​​of the angular velocities of each channel are all 0, and the deflection angles of the aircraft control surfaces are constrained. , , The control input constraint of the deformation actuator is The controller design parameters are detailed in Table 1.

[0076] Table 1

[0077] 4.1 Scenario 1: Reference Instruction Jump To evaluate the control effect of the designed nonfragile fuzzy controller based on the quantization switching mechanism, the following simulation scenario is set up.

[0078] Attitude angle command A three-stage step instruction sequence is used: Inside Simulated high angle-of-attack coordinated turning maneuvers during the climb phase; Internal switch to , , Simulated attitude adjustment during cruise phase; Further adjustments were made to the internal system. The simulation depicts a rapid roll maneuver during the descent phase. A smooth deformation command trajectory for descent, hold, and ascent is constructed using a sine square function. A complete deformation cycle is completed within a 20-second simulation duration. Furthermore, the selected disturbance is as follows: This includes cosine perturbations, sinusoidal perturbations, and constant biases to simulate common uncertainties in practice, such as aerodynamic parameter perturbations and wind disturbances. The initial state is as described above. Simulations were conducted under the aforementioned commands and disturbances, and the resulting time-domain response curves are shown below. Figure 3 As shown.

[0079] Figure 3The tracking performance for attitude angles and deformation rates is demonstrated. As shown in the figure, the proposed method exhibits excellent tracking performance for both attitude angles and deformation rates, and can respond quickly to changes in reference commands. The system has small tracking errors and high steady-state accuracy, meeting the accuracy requirements for attitude control of variator aircraft. For example, when switching between 6s and 12s commands, the angle of attack converges to the reference value within 1.5s, with a maximum tracking error of no more than 0.25° throughout the entire process. Overall, the proposed method can achieve tracking of multi-channel attitude and deformation commands, and maintains good dynamic performance even during command transitions.

[0080] Figure 4 The tracking curves for angular rates are shown. The attitude angular rate curve accurately tracks the virtual control law. For example, the pitch angular rate converges to its steady-state value within 1 second after a command switch, with a peak value of only 0.35 rad / s. (See the original text for detailed analysis.) 4.2 Scenario 2: Aerodynamic parameter deviation To verify the robustness and adaptability of the proposed method under more stringent conditions, this scenario, based on Scenario 1, further applies a larger bias error to the aerodynamic parameters to simulate modeling uncertainties that may occur in actual flight. Specifically, atmospheric density is introduced... The bias error introduces an effect on the moment of inertia. The bias error, while simultaneously injecting larger-amplitude composite disturbances into the system: This is to test the control quality of the controller under aerodynamic parameter mismatch and strong interference environment.

[0081] The attitude angle command uses a three-stage step sequence: Inside ; Internal switch to ; Further adjustments were made to the internal system. The deformation rate command is... A complete deformation cycle is completed within 20 seconds. All other initial parameters and simulation conditions remain the same as in scenario one.

[0082] The simulation was conducted under the above parameter configuration, and the resulting time-domain response curve is shown below. Figure 5 , Figure 6 and Figure 7 As shown.

[0083] Figure 5 The constraint envelope performance of the proposed FABLFs method was compared with that of the BLFs method. Figure 5As shown, the tracking errors of the angle of attack, sideslip angle, and deformation rate channels can be effectively constrained under both methods, and both transient and steady-state errors are within the constraint boundaries. For the angle of attack channel, at the 6-second command transition moment, because BLFs use a fixed constraint envelope, they cannot adapt to the rapid changes in the system's dynamic characteristics, resulting in significant fluctuations in the tracking error, which approaches or even exceeds the preset constraint envelope, leading to controller singularity. In contrast, FABLFs can adjust the constraint envelope in a timely manner when the tracking error approaches the constraint boundary, avoiding the risk of controller singularity. Figure 6 The curve of the upper bound estimate for the composite polynomial is shown. This demonstrates that the designed disturbance upper bound estimator can effectively estimate the upper bound of the composite polynomial. Even if a sudden change in command causes a tracking error, the estimate can be quickly adjusted, providing effective robustness assurance for the controller.

[0084] Figure 7 The output curves of the controller are shown. In the quantization switching mechanism, the system maintains mode 2 from 0 to 4s, switches to mode 1 as the deformation rate decreases at 4s and maintains it stably until 16s, and then switches back to mode 2 as the deformation rate increases. Within 4-16s, the deformation rate changes continuously but the mode remains constant, which can effectively avoid the chattering problem caused by frequent switching and improve the stability of system control. Figure 7 This is the output curve of the corresponding controller.

[0085] Simulation results of aerodynamic parameter deflection scenarios demonstrate that the proposed non-fragile fuzzy control strategy based on quantization switching mechanism is robust to model parameter uncertainties and can operate effectively in atmospheric density scenarios. Bias, Moment of Inertia Under bias conditions, it maintains good tracking accuracy and response speed; the constraint mechanism of FABLFs can effectively cope with the tracking error fluctuations caused by model uncertainty and avoid the constraint violation problem of BLFs; the disturbance upper bound estimator can compensate for unknown disturbances in real time, ensuring the stability and robustness of the system.

[0086] 5. Conclusion This paper addresses the model uncertainty, mode switching jumps, and vulnerability of traditional BLFs caused by deformation in HMVs under state constraints. A non-fragile fuzzy control strategy based on a quantization switching mechanism is proposed. The effectiveness of the proposed method is verified through Lyapunov stability theory and numerical simulations under two operating conditions. The main conclusions are as follows: Based on the quantization characteristics and switching logic of the modal partitioning variables, the designed quantization switching mechanism can quantize the continuous deformation process of HMVs into a finite number of discrete modes, establishing an HMVs model based on the quantization switching mechanism, providing a modeling foundation for the controller design of variator aircraft. By introducing FABLFs, the controller can achieve dynamic adaptive adjustment of the constraint envelope, avoiding the control output surge problem when the tracking error approaches the boundary, solving the controller singularity phenomenon caused by traditional BLFs, and improving the stability of the system under state constraints. By coupling external disturbances, fuzzy approximation errors, and the differential of the virtual control law into a composite polynomial and designing an upper bound estimator for disturbances, the system can compensate for unknown composite disturbances. Stability analysis and comparative simulations under two operating conditions—command jump and aerodynamic parameter deviation—verify the comprehensive performance of the proposed method in terms of mode switching, state constraint satisfaction, and anti-interference capability.

[0087] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit it. Although the present invention has been described in detail with reference to the above embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the specific implementation of the present invention. Any modifications or equivalent substitutions that do not depart from the spirit and scope of the present invention should be covered within the scope of protection of the claims of the present invention.

Claims

1. A non-fragile attitude control method for a variable-structure aircraft based on a quantization switching mechanism, characterized in that, include: The deformation amount of the variable-structure aircraft is obtained, and the deformation amount is quantized and discretized through a quantization switching mechanism to obtain different quantization modes; The outer loop state variables of the aircraft corresponding to the quantized modes are obtained, and the virtual control law is calculated based on the outer loop state variables. The outer loop state variables include angle of attack, roll angle, pitch angle and deformation rate. The virtual control law is designed based on the obstacle Lyapunov function for vulnerability avoidance. The inner loop state variables of the aircraft corresponding to the quantized modes are obtained, and the control variables are calculated based on the inner loop state variables; wherein the inner loop state variables include roll rate, yaw rate, pitch rate and deformation rate of change. The attitude of the modified aircraft is controlled by controlling variables.

2. The method according to claim 1, characterized in that, The quantization switching mechanism is as follows: ,in, This represents the quantization mode corresponding to time step t. Indicates the partitioning variable, This represents the deformation rate.

3. The method according to claim 1, characterized in that, The calculation process of the virtual control rate includes: ， in, This indicates the desired angular rate command output by the outer loop. For the first Tracking error of the outer loop state quantity of each channel For feedback gain, Nonlinear functions of the outer loop state variables For the online estimate of uncertainty, where The outer ring weight parameter is adjustable. For the basis function vector, For the upper bound of the composite polynomial, For the safety repulsion coefficient, This is the error amplification factor. This is the control gain matrix.

4. The method according to claim 3, characterized in that, The calculation of the virtual control law also includes the calculation of the adaptive law and the upper bound estimate; The adaptive law is as follows: ， The upper bound is estimated as follows: ， in, It is the estimated value of the fuzzy weight of the j-th channel. The rate of change, For adaptive learning rate, This is the error amplification factor. For fuzzy basis function vectors; It is the first Channel composite polynomial upper bound estimate The rate of change, Estimate the learning rate for the upper bound. and For the same error amplification factor, These are the adjustment parameters for the hyperbolic tangent function; subscripts j=1,2,3,4 correspond to the four channels: angle of attack, sideslip angle, roll angle, and deformation rate, respectively. Indicates the current quantization mode, through Adjustment ,pass Adjustment , will the and Calculate the corresponding virtual control law.

5. The method according to claim 1, characterized in that, The calculation process for the control quantity includes: ， in, To control the quantity, For the first The tracking error of the inner loop state variables of each channel. For feedback gain, Nonlinear functions of inner loop state variables For the online estimate of uncertainty, where The inner loop weighting parameter is adjustable. For the basis function vector, For the upper bound of the composite polynomial, This is the control gain matrix.

6. The method according to claim 5, characterized in that, The calculation of the control variable also includes the calculation of the corresponding adaptive law and upper bound estimate: The adaptive law is: ， The upper bound is estimated as follows: ， in, It is the estimated value of the fuzzy weight of the j-th channel. The rate of change, For adaptive learning rate, For the first The tracking error of the inner loop state variables of each channel. For fuzzy basis function vectors; It is the first Channel composite polynomial upper bound estimate The rate of change, Estimate the learning rate for the upper bound. These are the adjustment parameters for the hyperbolic tangent function; the subscripts j=1,2,3,4 correspond to the four channels of roll rate, yaw rate, pitch rate, and rate of change of deformation, respectively. Indicates the current quantization mode, through Adjustment ,pass Adjustment , will the and Calculate the corresponding virtual control law.

7. The method according to claim 1, characterized in that, The barrier Lyapunov function for vulnerability avoidance is: ， in, The barrier function for four state channels, real-time safety boundary. , Let be the constraint boundary function, where the constraint boundary exponential convergence rate is . The initial constraint boundary magnitude and the steady-state constraint boundary magnitude are respectively , This is an adjustment function with a correction term.

8. The method according to claim 7, characterized in that, Regulation function for: ， Among them, boundary adjustment gain Adjustment term decay rate Boundary trigger threshold coefficient These are design parameters.

9. A non-fragile attitude control system for a variable-structure aircraft based on a quantization switching mechanism, characterized in that, Used to perform the method described in any one of claims 1-8.

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